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Charge qubits in the ultrastrong coupling regime

Jiabing Yu, F. A. Cárdenas-López, Christian Kraglund Andersen, E. Solano, A. Parra-Rodriguez

Published May 14, 2021• 1 citation
OpenAlex

Abstract

We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound $|g|\leq \sqrt{\omega_q\omega_r}/2$ between two harmonic systems with frequencies $\omega_q$ and $\omega_r$. In our case, the fundamental model corresponds to an enhanced quantum Rabi model, which contains a displacement field operator that breaks its internal parity symmetry. Furthermore, we consider a multipartite device consisting of two CPBs ultrastrongly coupled to an oscillator as a mediator and study a quantum state transfer protocol between a pair of transmon qubits, all of them subjected to local incoherent noise channels with realistic parameters. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.

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Charge qubits in the USC regime for quantum state transfer

F. A. Cárdenas-López, Jing Yu, Christian Kraglund Andersen +2 more

Abstract We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We numerically show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound |g| ≤ √ωqωr/2 between two harmonic systems with frequencies ωq and ωr. As an application, we propose a hybrid system consisting of two CPBs ultrastrongly coupled to an LC-oscillator as a mediator device that catalyzes a quantum state transfer protocol between a pair of transmon qubits, with all the parties subjected to local thermal noise. We demonstrate that the QST protocol maximizes its efficiency when the mediator operates in the USC regime, exhibiting comparable times with proposals relying on highly coherent and controllable mediators requiring state-preparation or post-selection. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.

arXiv:2105.06851•May 14, 2021•1 citation

Ultrastrong light-matter interaction in quantum technologies

Simone Felicetti

In the last decades, the experimental and theoretical study of light-matter interactions in confined quantum systems has allowed to considerably widen and deepen our understanding of the quantum world.The simplest fully-quantized light-matter interaction is the quantum Rabi model (QRM), where a two-level system is coupled to a single bosonic mode.The implementation of quantum-optical systems in which the interaction strength overcomes losses brought a revolution to this research area.Under this condition, dubbed strong coupling (SC) regime, quantum processes can be observed at the single-photon level, and even exploited to perform Quantum Information tasks.Recent developments in solid-state Quantum Technologies have made possible to push the line further, achieving the ultrastrong coupling (USC) regime of the QRM, in which the interaction strength is comparable with the bare frequencies of the interacting systems.In the USC regime of the QRM, light and matter degrees of freedom merge into collective bound states called polaritons, the system ground state is not the vacuum and excitations are not conserved.The growing interest in USC-related phenomena is mainly motivated by the fundamental counterintuitive modifications to light-matter interactions entailed by this regime.At the same time, the USC regime is also expected to provide computational benefits in terms of operational speed, coherence time, and noise protection.In this Thesis, we theoretically analyze novel quantum phenomena emerging in the USC regime, which can be observed using nowadays technology and can motivate foreseeable improvements.The results here presented have been derived using two conceptually different approaches.On one side, we have analyzed interesting models that can be implemented in superconducting circuits, a quantum platform where the USC regime can be naturally achieved.In particular, we focused on excitation transfer across USC impurities, entanglement generation via modulation of electrical boundary conditions and quantum state engineering in ultrastrongly-coupled systems.On the other hand, we have developed methods to reproduce the physics of light-matter interactions in the USC regime, by tailoring the Hamiltonian of atomic systems, like trapped ions and cold atoms.These proposals take profit of the specific features of such quantum platforms, in order to implement regimes and measurements that are not directly accessible.We believe that this Thesis will contribute to develop a thorough understanding of quantum phenomena related to the USC regime of light-matter interaction, and that it will foster the dialog between experimental and theoretical research in this area.I would like to thank first my PhD supervisor Prof. Enrique Solano, for his constant support and invaluable guidance.Countless thought-provoking discussions held with him during my PhD studies have contributed to develop my critical skills, and his advice has covered all facets of nowadays top-level research.

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In this experiment, we couple a superconducting transmon qubit to a high-impedance $645\phantom{\rule{0.28em}{0ex}}\mathrm{\ensuremath{\Omega}}$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate $g$, measured through a large vacuum Rabi splitting of $2g\ensuremath{\simeq}910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $\ensuremath{\omega}$, placing our system close to the ultrastrong coupling regime ($\overline{g}=g/\ensuremath{\omega}=0.071$ on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong coupling $\overline{g}\ensuremath{\sim}0.45$ with transmon qubits.

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This thesis consists of two parts: the main part is a theoretical investigation of the ultrastrong coupling regime for atom-light coupling in superconducting circuits, and the second part is concerned with the development of a new high coherence flux qubit design. \n \nThe spin-boson model describes the interaction between a quantum two-level system and a continuum of bosonic modes. When the interaction strength becomes comparable to the system frequency, the system enters the ultrastrong coupling (USC) regime, where the rotating wave approximation breaks and the system dynamics need to be described nonperturbatively. Recently, the ultrastrong coupling has been achieved on a device consisting of a superconducting flux qubit coupled to an electromagnetic continuum, with the coupling strength being verified in experiments by the standard transmission method. The first project in this thesis aims to measure the dynamics of the spin-boson model in a direct and controllable way when the coupling strength is in the USC regime. We propose three experiments to measure the coherence of the two-level system including the relaxation and dephasing, and the the renormalized tunneling frequencies in the ultrastrong coupling regime. The controllable measurements are realized with a fast-switchable ultrastrong coupling system consisting of a two-loop flux qubit galvanically coupled to an open transmission line, flux bias and driving lines, and readout circuits. The design and model of the full device are presented. We demonstrate that the three proposed experiments can be well implemented based on the simulations of qubit properties and coupling strengths. \n \nThe second part of the thesis presents work on the design of a new type of capacitively shunted flux qubit. This work is motivated by improving qubit coherence time and anharmonicity, which is essential for speeding up qubit gates and enhancing the capability of quantum computing. It was demonstrated that adding shunting pads to flux qubits can drastically improve the coherence time and the reliability of qubit fabrication, but the CSFQ was shown with moderate anharmonicities. In this project, we present the a new design of CSFQ and its circuit model, which contains three Josephson junctions and three shunting pads. In experiments, the qubit spectroscopy matches well with the circuit model, which takes into account all the capacitances between the qubit and other circuits. The qubit is found to have both large anharmonicity A = ω₁₂ - ω₀₁ = 2π ⨯ 3.69 GHz, and high coherence with T₁ = 40 ± 5 µs. We also present experiments on the multilevel quantum control and multilevel relaxation measurement. We perform qutrit state tomography to reconstruct the full density matrix with the tomography fidelity reaching 99.2%. We are able to extract the time-dependent state populations for the relaxation process of a qutrit, and extract the exact transition rates between the three levels.

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Ultrastrong light-matter coupling (USC) gives access to exotic quantum phenomena and promises faster quantum gates, yet coherent time-domain control in this regime remains largely unexplored. Here, we realize USC in a hybrid system consisting of an InAs nanowire-based gatemon qubit coupled to a superconducting resonator. Spectroscopy reveals an avoided crossing that cannot be captured by the Jaynes-Cummings (JC) model, as well as photon-number-dependent transitions whose energies deviate markedly from the JC ladder expected in the strong coupling regime. Beyond demonstrating USC, we achieve time-resolved coherent control of the qubit and measure coherence times comparable to gatemons operating outside the USC regime. These results establish that hybrid semiconductor-superconductor qubits can retain coherent control in USC and provide a platform for exploring quantum dynamics and device concepts in this regime.

cond-mat.mes-hallCross-listedarXiv:2603.19438•Mar 23, 2026•0 citations
We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound ∣g∣≤ωqωr/2|g|\leq \sqrt{\omega_q\omega_r}/2∣g∣≤ωq​ωr​​/2 between two harmonic systems with frequencies ωq\omega_qωq​ and ωr\omega_rωr​. In our case, the fundamental model corresponds to an enhanced quantum Rabi model, which contains a displacement field operator that breaks its internal parity symmetry. Furthermore, we consider a multipartite device consisting of two CPBs ultrastrongly coupled to an oscillator as a mediator and study a quantum state transfer protocol between a pair of transmon qubits, all of them subjected to local incoherent noise channels with realistic parameters. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.
Abstract We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We numerically show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound |g| ≤ √ωqωr/2 between two harmonic systems with frequencies ωq and ωr. As an application, we propose a hybrid system consisting of two CPBs ultrastrongly coupled to an LC-oscillator as a mediator device that catalyzes a quantum state transfer protocol between a pair of transmon qubits, with all the parties subjected to local thermal noise. We demonstrate that the QST protocol maximizes its efficiency when the mediator operates in the USC regime, exhibiting comparable times with proposals relying on highly coherent and controllable mediators requiring state-preparation or post-selection. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.
In the last decades, the experimental and theoretical study of light-matter interactions in confined quantum systems has allowed to considerably widen and deepen our understanding of the quantum world.The simplest fully-quantized light-matter interaction is the quantum Rabi model (QRM), where a two-level system is coupled to a single bosonic mode.The implementation of quantum-optical systems in which the interaction strength overcomes losses brought a revolution to this research area.Under this condition, dubbed strong coupling (SC) regime, quantum processes can be observed at the single-photon level, and even exploited to perform Quantum Information tasks.Recent developments in solid-state Quantum Technologies have made possible to push the line further, achieving the ultrastrong coupling (USC) regime of the QRM, in which the interaction strength is comparable with the bare frequencies of the interacting systems.In the USC regime of the QRM, light and matter degrees of freedom merge into collective bound states called polaritons, the system ground state is not the vacuum and excitations are not conserved.The growing interest in USC-related phenomena is mainly motivated by the fundamental counterintuitive modifications to light-matter interactions entailed by this regime.At the same time, the USC regime is also expected to provide computational benefits in terms of operational speed, coherence time, and noise protection.In this Thesis, we theoretically analyze novel quantum phenomena emerging in the USC regime, which can be observed using nowadays technology and can motivate foreseeable improvements.The results here presented have been derived using two conceptually different approaches.On one side, we have analyzed interesting models that can be implemented in superconducting circuits, a quantum platform where the USC regime can be naturally achieved.In particular, we focused on excitation transfer across USC impurities, entanglement generation via modulation of electrical boundary conditions and quantum state engineering in ultrastrongly-coupled systems.On the other hand, we have developed methods to reproduce the physics of light-matter interactions in the USC regime, by tailoring the Hamiltonian of atomic systems, like trapped ions and cold atoms.These proposals take profit of the specific features of such quantum platforms, in order to implement regimes and measurements that are not directly accessible.We believe that this Thesis will contribute to develop a thorough understanding of quantum phenomena related to the USC regime of light-matter interaction, and that it will foster the dialog between experimental and theoretical research in this area.I would like to thank first my PhD supervisor Prof. Enrique Solano, for his constant support and invaluable guidance.Countless thought-provoking discussions held with him during my PhD studies have contributed to develop my critical skills, and his advice has covered all facets of nowadays top-level research.
In this experiment, we couple a superconducting transmon qubit to a high-impedance $645\phantom{\rule{0.28em}{0ex}}\mathrm{\ensuremath{\Omega}}$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate ggg, measured through a large vacuum Rabi splitting of $2g\ensuremath{\simeq}910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $\ensuremath{\omega}$, placing our system close to the ultrastrong coupling regime ($\overline{g}=g/\ensuremath{\omega}=0.071$ on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong coupling $\overline{g}\ensuremath{\sim}0.45$ with transmon qubits.
We study quantum state transfer between two qubits coupled to a common quantum bus that is constituted by an ultrastrong coupled light-matter system. By tuning both qubit frequencies on resonance with a forbidden transition in the mediating system, we demonstrate a high-fidelity swap operation even though the quantum bus is thermally populated. We discuss a possible physical implementation in a realistic circuit QED scheme that leads to the multimode Dicke model. This proposal may have applications on hot quantum information processing within the context of ultrastrong coupling regime of light-matter interaction.
This thesis consists of two parts: the main part is a theoretical investigation of the ultrastrong coupling regime for atom-light coupling in superconducting circuits, and the second part is concerned with the development of a new high coherence flux qubit design. \n \nThe spin-boson model describes the interaction between a quantum two-level system and a continuum of bosonic modes. When the interaction strength becomes comparable to the system frequency, the system enters the ultrastrong coupling (USC) regime, where the rotating wave approximation breaks and the system dynamics need to be described nonperturbatively. Recently, the ultrastrong coupling has been achieved on a device consisting of a superconducting flux qubit coupled to an electromagnetic continuum, with the coupling strength being verified in experiments by the standard transmission method. The first project in this thesis aims to measure the dynamics of the spin-boson model in a direct and controllable way when the coupling strength is in the USC regime. We propose three experiments to measure the coherence of the two-level system including the relaxation and dephasing, and the the renormalized tunneling frequencies in the ultrastrong coupling regime. The controllable measurements are realized with a fast-switchable ultrastrong coupling system consisting of a two-loop flux qubit galvanically coupled to an open transmission line, flux bias and driving lines, and readout circuits. The design and model of the full device are presented. We demonstrate that the three proposed experiments can be well implemented based on the simulations of qubit properties and coupling strengths. \n \nThe second part of the thesis presents work on the design of a new type of capacitively shunted flux qubit. This work is motivated by improving qubit coherence time and anharmonicity, which is essential for speeding up qubit gates and enhancing the capability of quantum computing. It was demonstrated that adding shunting pads to flux qubits can drastically improve the coherence time and the reliability of qubit fabrication, but the CSFQ was shown with moderate anharmonicities. In this project, we present the a new design of CSFQ and its circuit model, which contains three Josephson junctions and three shunting pads. In experiments, the qubit spectroscopy matches well with the circuit model, which takes into account all the capacitances between the qubit and other circuits. The qubit is found to have both large anharmonicity A = ω₁₂ - ω₀₁ = 2π ⨯ 3.69 GHz, and high coherence with T₁ = 40 ± 5 µs. We also present experiments on the multilevel quantum control and multilevel relaxation measurement. We perform qutrit state tomography to reconstruct the full density matrix with the tomography fidelity reaching 99.2%. We are able to extract the time-dependent state populations for the relaxation process of a qutrit, and extract the exact transition rates between the three levels.
Ultrastrong light-matter coupling (USC) gives access to exotic quantum phenomena and promises faster quantum gates, yet coherent time-domain control in this regime remains largely unexplored. Here, we realize USC in a hybrid system consisting of an InAs nanowire-based gatemon qubit coupled to a superconducting resonator. Spectroscopy reveals an avoided crossing that cannot be captured by the Jaynes-Cummings (JC) model, as well as photon-number-dependent transitions whose energies deviate markedly from the JC ladder expected in the strong coupling regime. Beyond demonstrating USC, we achieve time-resolved coherent control of the qubit and measure coherence times comparable to gatemons operating outside the USC regime. These results establish that hybrid semiconductor-superconductor qubits can retain coherent control in USC and provide a platform for exploring quantum dynamics and device concepts in this regime.